Mathematics of Music Composition

– A sentiment after the seventh round of Music Colloquium

Zark Browning, a Music Composition professor from University of Illinois at Urbana-Champaign, came to our Music Colloquium with a flutist and a pianist to give us a lecture on May 26, 2009. The topic was "Numbers and Music", as a matter of fact, focusing on Golden Sections and Magic Square.

At first, he provided different genres of music and scores, ranging from popular music to classical music, as evidence to prove the existence of Golden Sections and its effect. Then he introduced a composing method, Magic Square, which has been used in his works. Some of his compositions were played by human and machine simultaneously, but the latter one is only a recording, not an interactive program. One of the performers told us that it is always a challenge to play with an absolutely precise part without any cue especially on the connection point, whereas the composer said this kind of tension is tremendously fascinating. Finally, there was a small workshop after the colloquium. He showed the detail of his musical idea structure and let the pianist play each specific element.

"The characteristic feature of art of all kinds is that it combines objective criteria and methods with choice making. The difference between art and algorithm is that deterministic methodology (algorithm) always produces the same result from the same inputs, whereas nondeterministic methodology may produce variable results even with the same inputs." [2] Music, a kind of the nondeterministic methodology, may be something about numbers. Many people have been curious about their relationship for a long time.

Frankly speaking, I was somewhat disappointed with Professor Zark Browning's lecture. I appreciated his compositions but not the content of his speech. First of all, it might result from the topic title, "Numbers and Music". Since he actually wanted to talk about the numeric circumstances such as the ratio and the origin of chosen material, he may as well use "Numbers in Music".

On the other hand, as far as I am concerned, his examples of Golden Sections were little persuasive. The ratio seemed the same, but the context was very different in each piece. Therefore the influence was not surely significant. "Musical cognition implies the simultaneous recognition of a permanent and a changeable element...for the apprehension of music depends upon those two faculties, sense perception and memory; for we must perceive the sound that is present, and remember that which is past. In no other way can we follow the phenomenon of music." [1]

Last but not least, as a composer who loves to play numbers, he was supposed to bring us more mathematical and aesthetic perspectives, rather than several composing tools. "Mathematics is the result of mysterious powers which no one understands and in which the unconscious recognition of beauty must play an important part. Out of infinity of designs a mathematician chooses on pattern for beauty's sake and pulls it down to earth." [3] "Guido d'Arezzo's method shows his concern that music should be subordinate to the sacred Latin text. Schoenberg's combinatorial methods show a desire to deconstruct conventional harmonic expectation. Schillinger's methods followed from his desire to develop generative theories of art. Xenakis' statistical methods reflect his view of the quantum nature of sound. Cage's chance methods serve his aim to deconstruct the expectation of expectation." [2]

"The gulf between the arts and sciences has continued to this day. Some artists rail against reductionist explanations of creativity. Some scientists question whether aesthetic experimentation can be scientific. But methodological analysis reveals that the disciplines of art and science are cut from the same cloth. Comparing Euclid's method with Guido's method, we saw that they are distinguished only by the role of subjective choice–of nondeterminism–in art. Art is not science, but their methods are more alike than different. When applied to music, methodological criticism goes quickly to the core of the artist's intention, allowing us to apprehend the deeper significance of their art." [2]

To make a long story short, I believe that composers are scientists of music art, who have the responsibility to rehabilitate "it". Everyone also has to keep an open-minded learning on purpose to be a whole person. Not only might one narrow his vision, but he might also lose the meaning of being a human if he spends all time on the endless minor details from specific division of knowledge.

References
[1] Aristoxenus. "The Harmonics." in Macran, 1902, 27-30.
[2] Loy, Gareth. Musimathics. Cambridge, Massachuseets: The MIT Press, 2006.
[3] Morse, Marston. "Mathematics and the Arts." Bulletin of the Atomic Scientist, February, 1959.